Multiple choice

From a container of milk, $5$ litres of milk is replaced with $5$ litres of water. This process is repeated again. Thus in two attempts the ratio of milk and water became $81:19.$ The initial amount of milk in the container was

  1. $50$ litres
  2. $45$ litres
  3. $40$ litres
  4. $25$ litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial milk be x. After two replacements of 5L, final milk = x(1 - 5/x)^2. Ratio of milk to total is 81/100. So, (1 - 5/x)^2 = 81/100. Taking square root, 1 - 5/x = 9/10. 5/x = 1/10, so x = 50.

AI explanation

When a fraction equal to 5/V of the total initial volume V is replaced with water twice, the remaining fraction of milk is the square of 1 minus 5/V. This remaining fraction equals 81 divided by the sum of 81 and 19, which is 100, so the square of 1 minus 5/V equals 81/100. Taking the square root gives 1 minus 5/V equals 9/10, meaning 5/V equals 1/10. Solving for V gives an initial amount of 50 litres.

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